WE TEND to think that the three biggest problems with the standard model of particle physics are how it struggles to include gravity, the absence of a good dark matter candidate and (to some of us, at least) its inadequate explanation for the cosmic acceleration/dark energy problem. Otherwise, it is heralded as an incredibly successful model of physical reality that has, over and over again, been tested and verified through experiments.

Although it seems to describe only about 5 per cent of the universe’s matter and energy content, the standard model does explain three of the four fundamental forces: electromagnetism, the weak nuclear force and the strong nuclear force. It does all of this with just one equation. Simple enough, right?

But have you ever looked at that equation? There are so many parts in it that I was actually too lazy to count them all while writing this column. Instead, I resorted to estimating by counting the number of lines it took up (about 40) and estimating the number of major parts, which we call “terms,” that appeared on each line (about three). In other words, this is an equation with around 120 major components. Yes, that is 120 plus or minus signs.

It makes sense that the Lagrangian – the equation that describes the possible states of the standard model – is complex. After all, it is tasked with describing every fundamental particle we have ever observed in the lab: all six types of quarks, three types of neutrinos, the electron, the muon, the tau, the photon, the W and Z bosons, the gluon and the Higgs boson.

And it is easy to get the impression that because we are able to write down the equation that describes all of these particles and how they interact with each other at the most fundamental level, it is therefore easy to make calculations using the equation.

This is the opposite of the reality that we particle physicists find ourselves in. Completely solving an equation with this many terms is essentially impossible, and we usually have to figure out the conditions that allow us to ignore certain parts of the standard model in favour of the ones that matter for the calculation before us. Even then, we have to use special techniques to get actual numbers out.

“Completely solving an equation with as many terms as that of the standard model is essentially impossible”

The key question that comes up when we sit down to perform a calculation is whether we can apply a technique called perturbation. When we use a perturbation-based approach, we start with a simpler equation than our standard model terms.

This simpler equation can’t solve our problem, but it can help. Using carefully thought-through assumptions, we solve our more complicated problem by making small changes to the simpler equation. Most parts of the standard model can be handled using perturbative methods.

However, there is one area of the model where this doesn’t work so well: quantum chromodynamics (QCD). This describes strong nuclear force interactions, quarks and their mediating particles (gluons). Because of its unique features at low energies, QCD isn’t always amenable to perturbation.

As such, we have had to resort to other techniques. The most notable of these is known as lattice QCD. It is so named because instead of treating space as continuous with no gaps, in lattice QCD, space is treated as though it is a grid.

The specific challenges of describing QCD have recently become a bit newsworthy because of an exciting announcement from the Fermi National Accelerator Laboratory in Illinois. The researchers there looked at muons, which are electrically charged particles that spin when they are in a magnetic field.

However, rather than spinning at the speed predicted by the standard model, the measurements at Fermilab found that they were spinning a little too fast. This could suggest that there are particles beyond the standard model affecting the results, and it is therefore a tantalising idea!

But on the same day in April that the announcement was made, a paper was published in the journal Nature that proposed there is actually no mismatch between the standard model and current experiments. Instead, the authors propose a new approach to solving the equations that describe this particular phenomenon in the standard model.

In other words, they think that the experiments are fine and so is our model – the problem is our calculation techniques. Only time will tell who is right, but this prospect is a reminder that figuring out what is going on is more complicated than theorising beyond standard-model physics. We also need to fully understand how to calculate with the physics we have.